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Sma 200:Calculus Ii Question Paper

Sma 200:Calculus Ii

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2012

1

A Constituent College of Kenyatta University
UNIVERSITY EXAMINATIONS 2010/2011 ACADEMIC YEAR
4
TH YEAR 1ST SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF SCIENCE & BACHELOR OF EDUCATION SCIENCE

SMA 200- CALCULUS II
END SEMETER: I TIME: 3 HOURS
DAY/TIME: WEDNESDAY: 5.00 TO 8.00 P.M. DATE: 24/11/2010 (LTN)
INSTRUCTIONS: Answer Question ONE and any other TWO.
QUESTION ONE –[ COMPULSORY – 40 MARKS]
a) Find the indefinite integrals;
i) dx (4 marks)
ii) dx ( 3 marks)
iii) dx (3 marks)
b) The graph of y from (1,1) to (4,2) is revolved about the x-axis. Find the area of the
resulting surface.
(4 marks)
c) Find the integral dx
(5 marks)
d) i) Find the area under the curve y 2x- from x=0 to x=2
(3 marks)
2
ii) The region in (i) above is then revolved about the x-axis. Find the volume of the solid
formed.
( 4 marks)
e) Find the integral x dx
(3marks)
f) Find the integral dy (5 marks)
g) Find the integral
(6 marks)
QUESTION TWO – [15 MARKS]
a) i) State without proof the Fundamental Theorem of Calculus
(1 mark)
ii) Find the integral dx , by making the substitution t=
(7 marks)
b) i) Evaluate the definite integral dx ( 4 marks)
ii) Find the area of the region bounded by the graphs of and
(3 marks)
QUESTION THREE –[ 15 MARKS]
a) Find the indefinite integral dx (7 marks)
b) If , find the arc length of the graph of f from A( 8,2) to B ( 27,17).
(6 marks)
c) Determine whether the function is an even or odd function. (2 marks)
QUESTION FOUR –[15 MARKS]
a) Determine whether dx converges or diverges.
( 5 marks)
b) Approximate the integral dx using Simpson’s Rule with 8 subintervals
(5 marks)
c) Find the indefinite integral dx
(5 marks)

Sma 200:Calculus Ii Question Paper

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